1. Field of the Invention
The present invention relates to the field of pigment characterization. More specifically, this invention concerns a method and apparatus for determining the flake concentration and spectral absorption of pigments for paints containing metal flakes.
2. Related Art
The scattering of light from non-flake paints can be predicted by assuming that the incident radiation consists of a combination of collimated light (from directed sources, such as the sun) and diffuse radiation (from the sky or from surrounding surface reflections) and by modeling the paint as diffusely scattering pigments immersed in a binder. The resulting equations for the light intensity in the paint as a function of depth (called Kabulka-Munk equations) can be solved, and from the solutions the emergent light intensity is calculated. This emergent light is mostly diffuse reflection from the pigments, which gives the paint its color; but it also includes some directional, or specular, reflection from the paint finish, which gives the paint its gloss. The fact that the solutions for the reflected light are well-behaved functions of the pigment absorption suggests that by measuring the emergent diffuse light at a number of wavelengths one can identify the pigments in the paint from the spectral shape of the absorption, and one can identify the concentration of the pigments from the magnitude of the absorption. An extensive discussion of the Kabulka-Munk equations and applications thereof is provided in U.S. Pat. No. 5,231,472 to Marcus, et al., incorporated herein by reference.
The predicted relationship between the diffuse reflectance and the pigments can be verified with measurements, and recently the hardware necessary to make these measurements has been efficiently packaged into hand-held spectrophotometers which can measure the reflected light and calculate the pigment types and concentrations in a shop environment. Note that experimental verification of the theory at the laboratory level using scientific instruments is an essential element in the design of such a hand-held instrument for two reasons. First, one cannot rely on the theory to predict the pigment absorption as a function of reflected light to high accuracy, since the Kabulka-Munk model is an approximation of the true physics. The hand-held unit must have a accurate transformation between measured reflectance and pigment absorption stored in its memory. Thus, this transformation needs to be quantified experimentally, with the theory providing the ability to accurately interpolate between measurement points. Second, an instrument which measures the diffuse reflection by detecting the radiation coming off the sample over all non-specular angles is expensive and impractical for hand-held packaging. Thus, laboratory experiments must determine which subset of reflection angles characterize the diffuse scattering well enough to accurately determine the total diffusely reflected radiation.
Flake paints, in which aluminum flakes are mixed into the binder with the pigment, cannot be reliably characterized with these hand-held spectrophotometers, either in their pigment type and volume concentration or their flake volume concentration. This is because the presence of the flakes significantly alters both the specular reflection and the diffuse reflection. The increase in specular reflection is most significant, since the flake surfaces are relatively flat and aligned parallel to the paint surface and thus reflect in a specular manner. But the flakes also affect the diffuse reflection, since the specular reflections from the flakes can be forward scattered by the pigments out of the surface and since the flakes diffusely reflect any diffuse light that is incident upon them.
U.S. Pat. No. 5,231,472 to Marcus, et al. provides a method of characterization of metallic paints by representing the reflected and scattered light as having components from the following: light from the incident beam which is reflected by the metal flakes toward the observer; light scattered by the colored pigments which is reflected by the metal flake towards the observer; and light scattered by the colored pigments towards the observer. The method disclosed therein is an iterative method which attempts to minimize the error between reflection measurements made on sample and "trial" coatings, which are attempts at making a match.